Problem: Rewrite the function by completing the square. $f(x)=x^{2}+20x+40$ $f(x)=(x+$
Answer: We want to complete $x^2{+20}x$ into a perfect square. To do that, we should add $\left(\dfrac{{+20}}{2}\right)^2={100}$ to it: $x^2{+20}x+{100}=(x+10)^2$ In order to keep the expression equivalent, we add and subtract ${100}$, not forgetting the expression's constant term, $40$ : $\begin{aligned} f(x)&=x^2+20x+40 \\\\ &=x^2+20x+{100}+40-{100} \\\\ &=(x+10)^2+40-100 \\\\ &=(x+10)^2-60 \end{aligned}$ In conclusion, after completing the square, the function is written as $f(x)=(x + 10)^2 - 60$